This invention relates to a method and apparatus for performing arithmetic operations on binary digital numbers and more particularly to a method and apparatus for adding two binary digital numbers.
The current typical fast adder is the look ahead adder. Since the total number of logic gates of a look ahead adder is proportional to a quadratic function of n, the number of bits of the addends, the total number of logic gates of a look ahead adder will be very high when n is large. To limit the total number of logic gates, the typical look ahead adder integrated circuit has 4 bits. For the computation of binary numbers with more bits, 4 bit look ahead adder integrated circuits are typically connected in cascade. For example, a 64 bit adder is constructed by connecting 16 4-bit look ahead adder integrated circuits in parallel and has two more levels of carry propagation circuit. In other words, such an adder looks just 4 bits ahead.
Furthermore, the look ahead adder provides a particular propagation path for each carry which is generated by each pair of bits of the addends. For example, a 4 bit look ahead adder has 4 independent carry propagation paths. At most one of these 4 paths will be used to propagate a carry. Therefore, any two of these 4 independent paths cannot be electrically connected together. Otherwise, a digital value 1 and a digital value zero may exist on the same node which is an electrical disaster. Hence the output of the carry of the 4 bit look ahead adder must be selected from these 4 independent paths. Because of the requirement for an independent carry propagation path for each bit and the selection of the carries from these independent paths, the look ahead adder requires more gates and more time delay than the Isolated Carry Propagation Fast Adder of the present invention as will be subsequently explained. The adder of the present invention can create the necessary carry propagation paths, which depend only upon the binary digital value of the addends, without an electrical disaster. In other words, the carry propagation paths of look ahead adder are preconstructed in the hardware for each kind of carry, while the carry propagation paths of the present invention are constructed by electrically connecting and isolating the carry nodes according to the binary digital value of the addends. The meaning of the words "Isolated Carry Propagation" will be explained in detail later.